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This study compares two approaches (the average rainfall intensity method and the modified rational formula) for use with the rational formula with time-distributed rainfall events. Here, the average rainfall intensity method is used to consider the maximum mean rainfall intensity during the time of concentration for a basin around the peak rainfall such that the rational formula can be applied. This study considers artificial basins with times of concentration from 1 to 24 hours and a symmetric rainfall event time-distributed by the Yen & Chow model. The rainfall duration is assumed to be 12 hours to consider all the possible combinations of rainfall duration and time of concentration. The results can be summarized as follows. First, this study proposes a new method of applying a modified rational formula that considers the horizontally divided components of a rainfall event. This proposed method is effective in estimating peak flow and peak time. Second, the biggest difference between the applications of the average rainfall intensity method and the modified rational formula is evident when the rainfall duration is longer than the time of concentration. The applications of the average rainfall intensity method run the risk of underestimating the peak flow. However, this problem can be alleviated when the time of concentration becomes longer than the rainfall duration. Under the assumption of a basin with a rectangular shape, this difference nearly disappears. These findings are also confirmed in the other applications with different rainfall durations.

Application of the Modified Rational Formula to Time-Distributed Rainfall Events and Comparison with the Rational Formula Application